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PhD Dissertation of Stefanos Kozanis

This dissertation is referring to the exploration of non-linear problems of geotechnical engineering, with the use of the Finite Element Method (F.E.M). The problem on which this essay focuses is the anisotropy of the rock-mass, the exploration of constitutive models for anisotropic behaviour and the analysis of such problems with the Finite Element Method. The dissertation is divided in two parts. In the first part, the existing theories are presented. In the second part, the themes contains the originality of the dissertation are presented.

The first chapter is the introduction, where all the relevant terms, for the better understanding of the problem, are analysed. All the essential terms of the continuous medium mechanics and the linear-elastic nature of the anisotropy problem are shown here. Finally, it is shown how the anisotropic-behaving rock-mass is modeled like a continuous medium problem, in order to use on it the theories of elasticity in anisotropic medium.

On the second chapter, the Finite Element Methode is fully described, together with the new software, called x-fem, that was developed using the object oriented language C++, in Unix enviroment. All the essential algorithms and analysis methodology are fully presented here. The relevant codes and algorithms used in order to face anisotropic medium elasticity problems are shown. An elasticity problem is fully solved and the results are compared to the ones deriving from photoelasticity experiments.

The third chapter contains the elastoplastic-behaviour theory. Theories and yield or failure criteria used by the x-fem (like the von Mises or the Drucker-Prager one) are mentioned here. An algorithm and analysis code of elastoplastic problems are fully exhibited here. The criterion of paraboloid from revolution is given a new, x-fem, algorithm. The problem of elastoplastic behaviour of stress distribution on a horizontal plate with cuttings is fully solved and the experimental results are compared with those of the international bibliography.

The fourth chapter contains the rock-mass failure criteria that deal with the failure state of isotropic medium. A quick reference of Mohr-Coulomb, Griffith and Hoek-Brown criteria is essential. Several criteria concerning the anisotropic failure state of rock-mass are shown and special emphasis is given to Amadei's one, as its use (with an x-fem support) is proposed to many joint systems with anisotropic slipping.

On the fifth chapter, a geotechnical problem with elastic anisotropy gets completely solved and the results are compared with the closed-form solution ones.

In the sixth chapter, the anisotropic criterion of the elliptic paraboloid is presented and the widespread of its use is checked. A methodology and an algorithm for the elastoplastic analysis of orthotropic materials with the finite element method (and especially x-fem) are proposed. Finally, a demonstration problem of elastoplastic behaviour is treated.

On the seventh chapter, the expansion and full study of the Amadei criterion are considered. It's showed that the Amadei criterion equals the Mohr-Coulomb one from a certain amount of joint sets and onwards.

In the eighth chapter, the failure criterion of the elliptic paraboloid is proposed to be used to geotechnical problems and especially to anisotropic rock-mass ones. Firstly, the isotropic criteria of Hoek-Brown and of paraboloid of revolution are compared and their parabolic shape is shown. A special methodology, based on the rock-mass characteristics, for the calculation of the endurance parameters of the anisotropic criterion of the elliptic paraboloid is introduced. A comparison and a compatibility check of the slipping criteria (like Amadei's) with the elliptic paraboloid one are made. A special methodology and an analysis algorithm (with the use of finite element method) are proposed.

Some arithmetic solutions are presented in the ninth chapter, with the use of the elliptic paraboloid to geotechnic problems of anisotropic rock-mass and use of x-fem software. The first one is an arithmetic solution that is presented using real ground topography and the analysis is done on a 3D scale. The second, comes from the field of underground structures and especially from the tunnel drive domain.

The tenth chapter is on the parametric study of a circular tunnel driven in anisotropic rock. The elliptic paraboloid failure criterion is considered. The elastoplastic deformations and plastic zones are calculated using x-fem software.

Finally, the eleventh chapter contains the whole gist (propositions, ways of thinking, solutions) throughout all the preceeding chapters. A number of subjects and problems that need further research in the future is displayed..

Research Activities (in Greek)...